Question

determine whether quadrilateral abcd with vertices a(-4, -5), b(-3, 0), c(0, 2), and d(5, 1) is a trapezoid. step 1: find the slope of ab. the slope of ab is
step 2: find the slope of dc. the slope of dc is
step 3: find the slope of bc. the slope of bc is
step 4: find the slope of ad. the slope ad is
the quadrilateral is a trapezoid because
(note: dropdown options for slope of ab include -5, -1/5, 1/5, 5; graph of quadrilateral on coordinate plane is present)

Explanation:

Step1: Slope of AB

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points A(-4, -5) and B(-3, 0), $m_{AB} = \frac{0 - (-5)}{-3 - (-4)} = \frac{5}{1} = 5$.

Step2: Slope of DC

For points D(5, 1) and C(0, 2), $m_{DC} = \frac{2 - 1}{0 - 5} = \frac{1}{-5} = -\frac{1}{5}$.

Step3: Slope of BC

For points B(-3, 0) and C(0, 2), $m_{BC} = \frac{2 - 0}{0 - (-3)} = \frac{2}{3}$.

Step4: Slope of AD

For points A(-4, -5) and D(5, 1), $m_{AD} = \frac{1 - (-5)}{5 - (-4)} = \frac{6}{9} = \frac{2}{3}$.

A trapezoid has at least one pair of parallel sides (equal slopes). Here, $m_{BC} = m_{AD} = \frac{2}{3}$, so BC || AD.

Answer:

Step 1: 5
Step 2: $-\frac{1}{5}$
Step 3: $\frac{2}{3}$
Step 4: $\frac{2}{3}$
The quadrilateral is a trapezoid because it has a pair of parallel sides (BC and AD have equal slopes).